What is a composite transfer function?

[Ian_Brooks]

Homework Statement

Let F(z) = a0 + a1z-1 + a2z-2 denote the composite transfer function of the transmitter, channel and the matched filter in this ultra wide band system. Find a two tap digital equalizer Heq(z) = w0 + w1z-1 that approximates an IIR zero-forcing equalizer for F(z).

Homework Equations

The Attempt at a Solution

I just want to know what a composite transfer function is - i'll try the problem myself.

 

[The Electrician]

I would suppose that the 3 elements of the system you mentioned, namely the transmitter, the channel and the matched filter each have a transfer function of their own. The composite transfer function would be the overall transfer function of all three operating together.

 

[piercas]

A composite transfer function is a mathematical representation of a system that includes multiple components, each with their own transfer function. In this case, the transmitter, channel, and matched filter all have their own transfer functions, but they can be combined into one composite transfer function, denoted by F(z), which describes the overall behavior of the system. This allows us to analyze and design the system as a whole, rather than individually manipulating each component.

In the given problem, the composite transfer function F(z) is represented by a polynomial with coefficients a0, a1, and a2. This function describes the input-output relationship of the system, where the input is represented by the variable z and the output is represented by the value of F(z).

To approximate an IIR zero-forcing equalizer for F(z), we need to find a two tap digital equalizer, represented by Heq(z), which can counteract the effects of the composite transfer function and achieve a desired output. This is done by manipulating the coefficients w0 and w1 of Heq(z) to minimize the error between the desired output and the actual output of the system. This process is known as equalization and is commonly used in communication systems to improve the quality of the transmitted signal.